Step-by-step explanation:
because you're asking how to solve this, I won't say the answers to each box (but I think this might help)
you would solve this by plugging in the year (t) to the equation
(P = 0.173t - 345.8)
example:
(year = 2015)
P = 0.173(2015) - 345.8
P = 348.595 - 345.8
P = 2.795
(rounded to the nearest tenth: 2.8%)
hope this helps!!
(if there are any specific years that you want me to go through, please let me know, but I think you might figure this one out on your own :) )
A triangle has a height of 5 and an area of 60. Find the base.
Answer:
24
Step-by-step explanat
(-4x4+6+3/3)x6
What is the solution
Answer:___(-4x⁴+9)x⁶
3
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
\(m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} \)
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Which of the following ordered pairs is represented by a point located on the y-axis?
Select one:
a.(6,-6)
b. (3,3)
c. (0,8)
d. (-5,0)
Answer:
d (-5,0)
Step-by-step explanation:
If a point is located on the x-axis, then the y-coordinate is 0.
d is the only point that sits on the x-axis. I know this because it's y-coordinate is 0.
(0,8) is actually a point sitting on the y-axis.
A pair of dice are tossed Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 10
Solution
-
Question A:
The pair of dice has a total space f
\(6\times6=36\)- For the dice to give a total of at least 5, the possible combinations are:
\(\begin{gathered} (2,3),(3,2) \\ (2,4),(4,2) \\ (2,5),(5,2) \\ (2,6),(6,2) \\ \\ (3,3) \\ (3,4),(4,3) \\ (3,5),(5,3) \\ (3,6),(6,3) \\ \\ (4,4) \\ (4,5)(5,4) \\ (4,6)(6,4) \\ (4,1)(1,4) \\ (5,5) \\ (5,6)(6,5) \\ (5,1)(1,5) \\ (6,6) \\ (6,1)(1,6) \\ \text{ In total there are 30 possiblilities} \end{gathered}\)- Thus, we have the probability of choosing at least 5 as follows:
\(\frac{30}{36}=\frac{5}{6}\)Question B:
- A total of at lest 10 ihas the following possibilities:
\(\begin{gathered} (5,5) \\ (4,6),(6,4) \\ \\ (5,6)(6,5) \\ (6,6) \\ \\ \text{ There are 6 possibilities} \end{gathered}\)- Thus the probability of the second roll being a total of at least 10 is
\(\frac{6}{36}=\frac{1}{6}\)Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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A car travels 450km at 100km/h and 90km at 60km/h. Find its average speed?
Answer:
Average speed = 90 km/h
Step-by-step explanation:
Given that:
Distance covered at 100 km/h = 450 km
Time = \(\frac{Distance}{Speed}\)
Time = \(\frac{450}{100}=4.5\ hours\)
Distance covered at 60 km/h = 90 km
Time = \(\frac{90}{60}=1.5\ hours\)
Total distance travelled = 450 + 90 = 540 km
Total time taken = 4.5 + 1.5 = 6 hours
Average speed = \(\frac{Total\ distance}{Total\ time}\)
Average speed = \(\frac{540}{6}\)
Average speed = 90 km/hr
Hence,
Average speed = 90 km/h
For triangle ABC use the Triangle Proportionality Theorem to solve for x. Show all of your work for full credit.
Answer:
x=17
Step-by-step explanation:
See attached.
Because of the Triangle Proportionality Theorem,
24: (2x-4)+6
20: 2x-4
Cross multiply these two ratios
48x-96 = 40x-80+120
Isolate variable: 8x = 96-80+120
Solve: 8x = 136
x=17
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
isosceles triangle
Step-by-step explanation:
first by using corresponding angle theorem:
<A=<C
<A=50°
then by using exterior angle theorem:
<A+<C=<B(the outer angle)
50°+<C=<B,<B=180°-80°(angle B lies in a staight line)
<B=100°
50°+<C=100°
<C=50°
Find the equation of the line with slope 2 and y-intercept (0,−1).
Answer:
2x-y = 1
Step-by-step explanation:
Equation of the line is y-y1 = m (x-x1), where m is the slope and (x1,y1) is a point that lies on the line.
Equation of the given line is,
y-(-1) = 2 *(x-0)
y+1 = 2x
2x-y = 1
Understanding Dilations and Similarity
1. Each problem shows three figures. Two of the figures in each problem are similar,
with a center of dilation at X.
Draw lines to determine which two figures are similar.
a.
b.
2. Explain how you used lines to determine which figures are similar.
From the given diagram, figure A is similar to figure C.
The dilation of two figures are given in a figure.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From the figure given below,
a) Figure A is similar to figure C. We can see from point X the figure A is dilated to figure C.
b) Figure A is similar to figure B. We can see from point X the figure A is dilated to figure B.
Therefore, from the given diagram, figure A is similar to figure C.
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Frankie is saving up to have spending money for her family vacation. If Frankie's current monthly net pay is $490.00 and her monthly expenses are $396.90 what percent of her net pay is left for savings?
19%
23%
67%
81%
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Kaitlyn got a score of 79.7 this version has a mean of 73.7 and a standard deviation of 12.Pierce got a score of 237.2 this version has a mean of 227 and a standard deviation of 17.Norma got a score of 8.7 this version has a mean of 6.7 and a standard deviation of 0.8If the company has only one position to fill and prefers to fill it with the applicant who performed Best on the aptitude test which of the applicant should be offered the job
To compare each candidate score, we can convert each individual score to a z-score and compare them. The z-score is given by:
\(z=\frac{x-\mu}{\sigma}\)where x represents the actual score, mu represents the mean and sigma represents the standard deviation.
Calculating the z-score of each candidate, we haev:
\(\begin{gathered} z_{Kaitlyn}=\frac{79.7-73.7}{12}=0.5 \\ z_{Pierce}=\frac{237.2-227}{17}=0.6 \\ z_{Norma}=\frac{8.7-6.7}{0.8}=2.5 \end{gathered}\)The highest z-score is associated with the best performance.
The job should be given to Norma.
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kenji is raising baby kittens. their weights after three weeks are 12 ounces, 14 ounces, 15 ounces, 15, ounces and 14 ounces, what is the mean weight of the kittens????
Answer: 14 ounces
Step-by-step explanation:
To find the mean, we add up all the values and divide by the number of values.
\(\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces\)
how to find out a circumference of a circle
Answer:
Circumference of a circle = 2πr
Step-by-step explanation:
We have to know the,
→ method/formula to find the circumference of a circle.
Formula we use,
→ C = 2πr
Thus, the required answer is 2πr.
Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range.
f(x) =x^2 +12x+6
What is the vertex?
What are the x-intercepts?
What is the y-intercept?
what is the axis of symmetry?
Identify the function's domain
Identify the function's range.
The Vertex is : (-6, -30)
The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)
The Y-intercept is : (0, 6)
The Axis of symmetry is : x = -6
The functions Domain: is All real numbers
The Range is : All real numbers greater than or equal to -30.
To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.
To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)
In this case, a = 1, b = 12, and c = 6.
Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.
To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)
So, the vertex is (-6, -30).
To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)
Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.
Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).
The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)
Thus, the y-intercept is (0, 6).
The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.
The domain of the function is all real numbers since there are no restrictions on the possible input values of x.
To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.
Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).
As a result, the range of the function is all real numbers greater than or equal to -30.
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39. Solve for x. SHOW ALL WORK FOR FULL CREDIT m n 6x-4 112°
Answer:
x = 12
Step-by-step explanation:
6x - 4 and 112 are same- side interior angles and sum to 180° , that is
6x - 4 + 112 = 180
6x + 108 = 180 ( subtract 108 from both sides )
6x = 72 ( divide both sides by 6 )
x = 12
Answer:
x = 12
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).
Therefore:
⇒ 6x - 4 + 112 = 180
⇒ 6x + 108 = 180
⇒ 6x + 108 - 108 = 180 - 108
⇒ 6x = 72
⇒ 6x ÷ 6 = 72 ÷ 6
⇒ x = 12
Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
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Answer:
Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
Step-by-step explanation:
Let \(x\) denote the number of rafts seating 3 people and \(y\) the number of rafts seating 5 people. The total number of rafts is 13, so \(x+y=13\). We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so \(3x+5y=53\).
It's always a good idea to put these equations under each other:
\(\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.\)
We can subtract the first equation three times from the second one to obtain \((3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7\)
Now, substitute this found value for \(y\) into \(x+y = 13\) and we see that \(x=6\). We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
................... rafts
Given: 1 yard = 3 feet
yards = 4 feet
Answer:
12
Step-by-step explanation:
4 times 3 = 12
Which of the following represent a linear inequality in open-sentence form?
(Select all that apply.)
2x - 7y > 10
3 < 5
2x + 8 = 10y
8 + x > 5
The linear inequality in open-sentence form is:
2x - 7y > 10
This is a linear inequality because it represents a relationship between variables (x and y) raised to the first power, combined with coefficients (2 and -7) and involves the inequality symbol (>).
The other options do not represent linear inequalities in open-sentence form:
3 < 5 is a simple numeric inequality without variables.
It compares two constant values and does not involve any variables or coefficients.
2x + 8 = 10y is an equation, not an inequality.
It equates the left side to the right side using an equal sign (=), indicating that both sides are equal.
8 + x > 5 is a linear inequality, but it is not in open-sentence form as it has an equation on one side (8 + x = 5) instead of just variables and constants.
The inequality symbol (>), in this case, is not appropriately used to represent the relationship between the variables.
The inequality 2x - 7y > 10 represents a linear inequality in open-sentence form among the given options.
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Please see my question in the attachment, thanks
As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.
In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;
As x → -1⁻, f(x) → ∞.
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Solve the equation. Check the solution. -2/x+4 =4/x+3
Equations are expressions with equal values
The solution of the equation is -11/3
How to determine the solutionThe equation is given as:
\(\frac{-2}{x + 4} = \frac{4}{x + 3}\)
Cross multiply
\(-2x - 6 = 4x + 16\)
Collect the like terms
\(-4x - 2x = 16 + 6\)
Evaluate the like terms
\(-6x =22\)
Divide through by -6
\(x =-\frac{11}{3}\)
Hence, the solution of the equation is -11/3
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Answer: \(-\frac{11}{3}\)
Step-by-step explanation:
HELP PLEASEEEEEEEE I NEED HELP ASAP
Answer: Fish tank = 9 other fishtank= 9,000 Jewlery box=9 other jewelry box=320
CANT SEE OTHER SORRY
Step-by-step explanation: Ok first IK UR NOT IN COLLEGE second dont
cheat imma give ya answer to be noice
Simplify the expression: 4a - 2b + 3a - 5b + 1
Answer:
7(a-b)+1 or 7a-7b+1
Step-by-step explanation:
Start by combining like terms and you will have 7a-7b+1
If you want to take it one step further you can pull the 7 from both like 7(a-b)+1
if a and b are consecutive even integers, where aa) 2a+1
b)2a^2+2b
c)3a^2+3b^2
d)2a+3b^2
e)2a+3b
The formula that can be used to illustrate consecutive even numbers is a + 2.
How to illustrate the information?It should be noted that the information is incomplete. Therefore, an overview will be given.
It should be noted that consecutive even numbers we the numbers that follow each other and have a difference of 2.
Examples of such numbers include 2, 4, 6,8, 10, etc.
In this case, the formula that can be used to illustrate consecutive even numbers is a + 2.
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Which expression is equival 81 1/3?
Answer: 3^3 Square root 3
Step-by-step explanation:
While reviewing the previous day’s arrest report, a police sergeant notices that five suspects were arrested, all of whom had either one or two previous arrests. Including yesterday’s arrests, there were 12 total arrests among them. How many suspects had less than two prior arrests?
The number of suspects had less than two prior arrests are 3.
Given that, While reviewing the previous day’s arrest report.
Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.
Here, x+y=5 -----(i)
2x+3y=12 -----(ii)
From equation (i), x=5-y in equation (ii), we get
2(5-y)+3y=12
10-2y+3y=12
10+y=12
y=2
Substitute y=2 in equation (i), we get
x+2=5
x=3
Therefore, the number of suspects had less than two prior arrests are 3.
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Which of the following tables represents a linear function? x −4 −1 0 1 2 y −4 2 −4 0 2 x 1 1 1 1 1 y −3 −2 −1 0 1 x −6 −1 0 2 3 y −7 negative sixteen thirds −5 negative thirteen thirds −4 x −2 −1 0 2 4 y −4 negative two thirds −1 two thirds 1 Question 5(Multiple Choice Worth 5 points) (Experimental Probability MC) A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks? one fifth 10 25 35 Question 6(Multiple Choice Worth 5 points) (Identifying Functions LC) The graph represents a relation where x represents the independent variable and y represents the dependent variable. a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma negative 1, at 0 comma 2, at 1 comma 3, and at 5 comma 1 Is the relation a function? Explain. No, because for each input there is not exactly one output. No, because for each output there is not exactly one input. Yes, because for each input there is exactly one output. Yes, because for each output there is exactly one input. Question 7(Multiple Choice Worth 5 points) (Line of Fit MC) A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data. scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 30, 1 comma 40, 2 comma 34, 3 comma 24, 3 comma 30, 4 comma 18, 5 comma 15, 5 comma 24, 6 comma 4, 6 comma 20, 7 comma 10, and 8 comma 0, with a line passing through the coordinates 3 comma 26.7 and 7 comma 7.66 Find the y-intercept of the line of fit an
The y-intercept of the line of fit is approximately 43.94 fluid ounces.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.
No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.
The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.
Therefore, The y-intercept of the line of fit is approximately 43.94 fluid ounces.
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Somebody please help me
The measure of the angle ∠BGC will be 37°.
What is the alternate interior angle?The alternate interior angles are the angles formed inside two parallel lines when they are intersected by a transversal and are equal to their alternate pairs.
Given that the angle ∠AGD is 37°. At this point, the line is making two angles one is ∠AGD and the just opposite angle is ∠BGC.
The two angles are opposite to each other so the angles will be equal to each other.
∠AGD = ∠BGC = 37°.
Therefore, the measure of the angle ∠BGC will be equal to 37°.
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